scholarly journals Calculating the Energy Spectrum of Complex Low-Dimensional Heterostructures in the Electric Field

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Svetlana N. Khonina ◽  
Sergey G. Volotovsky ◽  
Sergey I. Kharitonov ◽  
Nikolay L. Kazanskiy
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Ground State ◽  
State Energy ◽  
Airy Functions ◽  
Piecewise Constant ◽  
Matrix Rank ◽  
The Matrix ◽  
Constant Potential ◽  
Low Dimensional

An algorithm for solving the steady-state Schrödinger equation for a complex piecewise-constant potential in the presence of theE-field is developed and implemented. The algorithm is based on the consecutive matching of solutions given by the Airy functions at the band boundaries with the matrix rank increasing by no more than two orders, which enables the characteristic solution to be obtained in the convenient form for search of the roots. The algorithm developed allows valid solutions to be obtained for the electric field magnitudes larger than the ground-state energy level, that is, when the perturbation method is not suitable.

POLARON IN A QUANTUM DOT UNDER AN ELECTRIC FIELD

2007 ◽  
Vol 21 (24) ◽  
pp. 1635-1642
Author(s):  
MIAN LIU ◽  
WENDONG MA ◽  
ZIJUN LI
Keyword(s):  
Quantum Dot ◽  
Electric Field ◽  
Field Intensity ◽  
Ground State Energy ◽  
Ground State ◽  
Electric Field Intensity ◽  
State Energy ◽  
Theoretical Study ◽  
The Moment ◽  
Transformation Methods

We conducted a theoretical study on the properties of a polaron with electron-LO phonon strong-coupling in a cylindrical quantum dot under an electric field using linear combination operator and unitary transformation methods. The changing relations between the ground state energy of the polaron in the quantum dot and the electric field intensity, restricted intensity, and cylindrical height were derived. The numerical results show that the polar of the quantum dot is enlarged with increasing restricted intensity and decreasing cylindrical height, and with cylindrical height at 0 ~ 5 nm , the polar of the quantum dot is strongest. The ground state energy decreases with increasing electric field intensity, and at the moment of just adding electric field, quantum polarization is strongest.

THE INFLUENCE OF ELECTRIC FIELD ON THE GROUND-STATE LIFETIME OF POLARON IN A PARABOLIC QUANTUM DOT

2011 ◽  
Vol 25 (03) ◽  
pp. 203-210
Author(s):  
WEI-PING LI ◽  
JI-WEN YIN ◽  
YI-FU YU ◽  
JING-LIN XIAO
Keyword(s):  
Quantum Dot ◽  
Electric Field ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Phonon Coupling ◽  
Phonon Interaction ◽  
Strong Electron ◽  
Electron Phonon Interaction ◽  
Parabolic Quantum Dot

The ground-state energy of polaron was obtained with strong electron-LO-phonon coupling by using a variational method of the Pekar type in a parabolic quantum dot (QD). Quantum transition occurs in the quantum system due to the electron-phonon interaction and the influence of temperature. That is the polaron transition from the ground-state to the first-excited state after absorbing a LO-phonon and it causes the changing of the polaron lifetime. Numerical calculations are performed and the results illustrate the relations of the ground-state lifetime of the polaron on the ground-state energy of polaron, the electric field strength, the temperature, the electron-LO-phonon coupling strength and the confinement length of the quantum dot.

Matrix Elements of the Spin–Orbit Coupling for an ln Configuration in a Crystalline Electric Field

1972 ◽  
Vol 50 (2) ◽  
pp. 78-83 ◽  
Author(s):  
H. A. Buckmaster ◽  
R. Chatterjee ◽  
Y. H. Shing
Keyword(s):  
Electric Field ◽  
General Expression ◽  
Ground State ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Crystalline Electric Field ◽  
State Splitting ◽  
The Matrix

A general expression for the matrix elements of the spin–orbit coupling for an ln configuration in a crystalline electric field of arbitrary symmetry is derived using Racah formalism. This calculation is an extension of Lulek's treatment of this problem for an l1 configuration. This general expression is used to calculate the contribution to the ground-state splitting for the S-state lanthanide ion Gd3+ (4f7; 8S7/2)in an axial crystalline electric field of a second-order perturbation mechanism involving the matrix element of the spin–orbit coupling. It is shown that this mechanism, which was proposed by Lulek is incapable of explaining the observed ground-state splitting.

The ground state energy of the ±J spin glass from the genetic algorithm

1994 ◽  
Vol 4 (9) ◽  
pp. 1281-1285 ◽  
Author(s):  
P. Sutton ◽  
D. L. Hunter ◽  
N. Jan
Keyword(s):  
Genetic Algorithm ◽  
Spin Glass ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy
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